International Journal of Information & Computation Technology. ISSN 0974-2239 Volume 5, Number 1 (2015), pp. 1-10 © International Research Publications House http://www. irphouse.com Signing Multiple Messages using MD6 Hash Algorithm S. S. Hatkar1, T.R.Sontakke 2, A. M. Fajge 3 1 Associate Prof., Dept. of CSE,SGGSIE&T, Vishnupuri,Nanded-431606, India [email protected] 2 Ex. Director, SGGSIE&T, Vishnupuri, Nanded-431606, India [email protected] 3 M.Tech Student, Dept. of CSE, SGGSIE&T, Vishnupuri, Nanded-431606, India [email protected] Abstract In this paper we introduced an approach for signing multiple messages using MD6 hashing. Merkle‟s signature scheme is studied and implemented for a binary tree. This approach is simple to implement, and can resist the attacks that are even made with the help of quantum computer. Both the sizes of the signature are compared generated by proposed approach and Merkle‟s approach. Overall the space required for signature size of proposed algorithm is reduced as compared to Merkle‟s signature size. The size of the path information and number of hash operations that are required for verification of Merkle‟s public key are also reduced. Experimental results are compared and show that our approach is more computational efficient. Keywords: quantum computing, post-quantum cryptography, asymmetric key, digital signature algorithm, hash-based cryptography, merkle tree signature, elliptic curve cryptography. 1. Introduction Cryptographic schemas such as Digital Signature Algorithm, Diffie-Hellman on Elliptic Curves, Elliptic Curve Digital Signature Algorithm (ECDSA), and ElGamal Cryptosystem [1][2][3] are vital components of IT-security solutions. The problem is how can sender signs a message such that receiver can verify the digital signature which is good enough also for legal purposes. Digital signature schemas with this feature have many advantages, including smaller bandwidth for signatures on small message and direct integration into other schemas such as ElGamal encryption, identity-based public key systems or key agreement protocols. Handwritten signature 2 S. S. Hatkar et al appeared to be same for different documents, while digital signatures of the messages vary from message to message. At the time of sending necessary message, Signer generates signature using signing algorithm and in response to that Verifier uses verification algorithm for verification of the received message by validating received digital signature. When message m is signed, by X so that any Verifier can verify the signature as Sx(m) by using a public-key cryptosystem. When a message m is signed by a user X so that only Verifier Y can verify the signature; EY(SX(m)). Sending a message m and a signed hash value of m with the help of hash algorithm as: (m, SX(H(m))). Digital signature should not expose any information about how to generate copies of the signature on the behalf of the Signer. Modified version of the ElGamal digital signature schema was proposed in August 1991as DSA and adopted in December 1994. Security of the ElGamal signatures resides on the hardness of solving the discrete logarithm problem. Since ElGamal signature is unsecure than discrete logarithm, it is essential to increase the parameter size while signing the message using ElGamal signature algorithm which results in large signature size. Factorization problem may occur during signing a message by using public key cryptosystem. Shor[4] developed quantum algorithms which can solve integer factorization problem and discrete logarithmic problem [5] in bounded error quantum polynomial time (BQP) on quantum computer. A quantum computer is the device, which exploits the laws of quantum physics, such as superposition and entanglement, to process information. The idea of a quantum computer was first proposed in 1981 by American theoretical physicist Richard Feynman and Paul Benioff independently. Nobel laureate Richard Feynman pointed out that “Accurately and efficiently simulating quantum mechanical systems would be impossible on a classical computer, but that a new kind of machine, a computer itself built of quantum mechanical elements which obey quantum mechanical laws, might one day perform efficient simulations of quantum systems [6]”. Since the several key enhancements have been made in quantum computing, post-quantum cryptography has become a topic of research such as the invention of quantum algorithms, and quantum computers in the last few years. Many Cryptosystem protect data from stealing or modification, and can also be used for verification of the users. There are some specific security requirements such as authentication, integrity, privacy, and non-repudiation in any application-to-application communication. Complex cryptosystems which are in existence today are relying on the hardness of certain mathematical problems such as integer factorization problem and discrete logarithm problem. So, these cryptosystems are not provably secure since the mathematical structure of the problem is not provably hard. Therefore the security schemas, which are most widely used today, have implementation based on these problems and remain secure over the past years due to the fact that there is no known classical algorithm which can solve these problems in polynomial time. Shor‟s algorithm boosts the development of quantum computer and post-quantum cryptosystems. Quantum computer deals with thousands of qubit, can make current cryptosystems which rely on integer factorization problem and discrete logarithmic problem vulnerable. There are few more public-key cryptographic techniques for Signing Multiple Messages using MD6 Hash Algorithm 3 which no known efficient quantum algorithm exists, and which remain intact against the attacks performed with quantum computers, and systems which implement these post-quantum cryptosystems. One-Time signature (OTS) system is gaining more attention because of their post-quantum security and their appropriateness for compact implementations. This systems which is used to sign single message and general purpose signature systems for signing multiple messages, have been well-known since 1979 [7], and have advanced from renewed development in the last decade. This signature system provides asymmetric message authentication. It produces a public/private key-pair and the generated message signature can be verified using OTS public key. The rest of paper is organized into five sections. Second section describes the work related to OTS systems, Third Section elaborates the Merkle‟s Tree Signature (MTS) to solve problem of large public key size to sign multiple messages. Fourth section deals with the novel approach for minimizing the signature size, which helps to improve the space/time trade-offs of general purpose signature systems. In the fifth section, we discussed the results compared with MTS and in the last section the paper is concluded with some observations. 2. Signature Schemas One-Time Signature systems were well considered from 1990 and have advanced from new development over the last decade. The security of One-Time Signatures is based on cryptographic secure hash functions. A hash function H is cryptographic secure, if it is preimage resistant, second preimage resistant and collision resistant. The schemas called post-quantum signature have not depend on number theoretic problems to ensure security and come with the modularity in selecting hash function, and it is not tied to any specific hash function as that of traditional signature. Lamport proposed Lamport-Diffie One-Time Signature schema (LD-OTS) detailed in [8]. it is a signature scheme in which the public key can only be used to sign a single message. The security of the LDOTS is based on cryptographic hash functions. Any secure hash function can be used, which makes this signature scheme very adjustable. If a hash function becomes insecure it can easily be exchanged by another secure hash function. In this approach, Signer selects the two random values say, „X‟ and „Y‟ which serve as the key pair, and publishes H(X) and H(Y) as public keys. In the signature generation phase signer has to compute the hash of the message m, i.e. H(m) and for each bits of H(m), the signer then exposes i‟th bit H(X) if i‟th bit of H(m) is 0, and i‟th bit H(Y) otherwise. It is impossible for adversary to forge such signature without inverting selected one-way function. The large memory requirement of the original one-time signature schema makes schema impractical for general use. This is for the one bit message, however, it is insecure to use same „X‟ and „Y‟ key pair values for different messages, since it was found that, the one-time use of the signature exposes the half of the signing key once it used. The security of this schema depends on function „H‟, i.e. selected one way Hash function which states that, it is impossible to generate two different valid messages m1 and m2 for a given collision resistant hash 4 S. S. Hatkar et al function, say H, such that H(m1) = H(m2). Some of the hash functions designed to be remains secure even in presence of quantum computer, for example, SWIFFT in [9]. The main disadvantages of the single bit version of LD-OTS schema are- the size of the signature which found to be relatively large; it is not an efficient to generate the message signature of very large message, since it processes bitwise; and it does not allow signing multiple messages. To overcome the problem of signing large messages, Lamport One-Time Signatures multi-bit version is used. here, sender selects random values X [ X0, X1, X2, X3…, X255] and Y [Y0, Y1, Y2, Y3…, Y255] and publishes the set of the public key, such as, [H (X0), H (X1), H (X2), H (X3)…, H (X255)] for X and [H (Y0), H (Y1), H (Y2), H (Y3)…, H (Y255)] for Y. Sender can use these public keys to sign arbitrarily long message, m, efficiently by running many instances in parallel.